Supplementary Figure 5: Comparison of categorical and continuous decoders | Nature Neuroscience

Supplementary Figure 5: Comparison of categorical and continuous decoders

From: Decoding subjective decisions from orbitofrontal cortex

Supplementary Figure 5

The value assigned to the single pictures is categorical in nature, but the concept of value likely exists on a continuous scale. Therefore, we determined whether a linear model that estimates value on a continuous scale would perform better than the LDA, which attempts to discriminate discrete categories. (a) Each picture value was associated with a different distribution of decoded values, and these distributions were overlapping. Histograms of continuous value estimates decoded with a linear model from single picture trials in both subjects (n = 22845 trials). Each observation is a trial, and trials were grouped according to the value of the picture the subject was shown. Regressions of decoded value on actual value were highly significant for all sessions (minimum r2 = 0.16, maximum p = 1.32 x 10-20; median r2 = 0.49, median p = 1.7 × 10-79). (b) Confusion matrices from categorical and continuous decoders. The linear model performed similarly to the LDA (48% versus 44%, where chance = 25%), but tended to make different types of errors. The linear model had a greater tendency to confuse adjacent categories but distinguish non-adjacent categories. (c) Table of sensitivities and specificities for decoding each comparison with LDA or a linear model. The first column shows the value comparisons being tested. Red = better performing decoder. We directly assessed each model’s ability to delineate pairs (or triads) of adjacent categories by calculating the sensitivity and specificity of the categorization. Sensitivity is the hit rate (correctly identifying a given category when it is present) and specificity is the correct rejection rate (correctly identifying a given category is not present). Overall, the linear model performed worse, with lower sensitivities and specificities than the LDA for adjacent categories. Thus, the linear model’s assumption of no categories resulted in a poorer ability to resolve the categorical nature of the training data, and increases the bias toward confusing neighboring values. Given this, we used the categorical LDA to analyze choice trials.

Back to article page